The method of upper and lower solutions is a main tool to prove the existence of periodic solutions to periodic differential equations. It is known that, in general, the method does not extend to the almost periodic case. The aim of the present paper is to show that, however, something interesting survives: if the classical assumptions of the method are satisfied, then the expected existence result holds generically in the limit periodic framework.
Limit periodic upper and lower solutions in a generic sense / M. Tarallo, Z. Zhou. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 38:1(2018), pp. 293-309.
Limit periodic upper and lower solutions in a generic sense
M. Tarallo;
2018
Abstract
The method of upper and lower solutions is a main tool to prove the existence of periodic solutions to periodic differential equations. It is known that, in general, the method does not extend to the almost periodic case. The aim of the present paper is to show that, however, something interesting survives: if the classical assumptions of the method are satisfied, then the expected existence result holds generically in the limit periodic framework.
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